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Sunday, October 26, 2008

Is Curling a Battle for the Hammer?

Back during the era of the Grand Old Game; before push brooms, The Ryan Express and Shorty Jenkins ice moved us all to Free-Guard Zone; it was often heard at most every club by players at every level (of play and inebriation) that “Curling is a battle for the hammer”. To some degree this may have been true, though the strategies of teams like Savage and Werenich, Burtnyk and Olson and the Howard brothers opposed this mentality with their aggressive play. Rather than “Take 2 then Give 1”, these Superteams preferred to put constant pressure, take many and then steal until the opponent shook hands.

The question I raise is, in Today’s 4-rock game, is it still possible that Curling can be a Battle for Hammer? In my analysis, I will touch on several areas and provide some data which may help us find and answer.

The Hammer Advantage
Starting with hammer is an advantage. We know this because every time your team wins the toss, you don’t think too long about whether or not to choose stone colour. I expect some Ontario folks will shout out “I remember this one time so and so knew the rocks were bad and chose colour instead of hammer” – but I expect this is not a common occurrence.

The “draw to middle” or pre-selecting number of games in a round-robin where teams get hammer also indicates its importance.

We also have some data which tells us how often the team beginning with hammer wins. Unfortunately not all events keep proper track of who started the game with hammer and our sample size is not as large as we would like. One way to take a sample of data is looking at 10 end games that are tied after 2 ends (i.e. now an 8 end game). Our results show us a 61% winning percentage.

This doesn’t tell us much more than we already know, except to help us understand if 8-end games are fair. That is not, however, the purpose of this article (though we may return to this idea).

The Early Game
I believe Curling, sometimes called “Chess on Ice”, has an Early, Middle and an End Game (no pun intended, honest). End Game is the final 3 ends and extra end if required. The Middle Game is the middle 3 ends and the Early game is then either 4 ends for a 10 end game or 2 ends for an 8 end match. I haven’t chosen these game sections based on my best guess or what I’d like them to be, I’ve looked at the numbers and they reveal something very interesting:

The Odds of winning at the completion of each end during the Early game is nearly equal.

This is a fascinating discovery that not only explains why the Early Game doesn’t end until 6 ends remain in the game, but supports the theory that an 8 end game is competitively equal to a 10 end game. If you extrapolate the numbers, we might be even safe in assuming 12 ends or even 14 would also have the same outcome. The only benefit of a longer game (other than perhaps more beverage sales to the fans) is that the more ends played, the greater advantage a stronger team will have over a weaker team. The analysis behind that theory is not the purpose of this discussion, so back to where we were…

Middle Game
Odds of winning during the Middle Game start to trend in a specific direction.

End Game
Odds of winning in during the End Game trend steeply in one direction. The exception is 1 down with hammer, which drops then rises before the final end.

This graph best shows this trend:

Some comments:

Tied with hammer: Winning percentage is within 60-62% until 3 ends remain where it jumps more dramatically to 65%. That is, a tie game has nearly the same statistical outcome for all ends until the End Game is reached (starting the 6th or 8th).

1 down with hammer: Maintained around 42-43% until 5 ends remain, where drops to 39% in the Middle Game. It then rises back over 40% and during the End Game, 1 down winning percentage drops to 38%, then down below 35% and back above 38%. This phenomenon was discussed in the article “To go for two… or not? Masters of Curling final: Howard vs. Ferbey” from Black Book of Curling 2007-08.

Two down with hammer shows 27 to 26 % during Early Game than a drop below 25% beginning the Middle Game and a drastic drop to 20% with 4 ends remaining.

3 down with hammer: Stays around 15% until 6 ends remain then drop to 13%, then flat at 11 to 10% with another drastic drop beginning the End Game of below 7%.

1 up with hammer: Stays fairly constant, from 75% then leveling in the range of 77-80% until the End Game begins and it jumps to 84%.

The other scenarios are not as common, but do have some interesting results:

4 down with hammer: Transitions, oddly enough: 9-7-7-5-4-3-2-1-0%. Short answer – don’t be 4 down after the Early Game or you’re screwed.

2 up with hammer: 87-90% until we reach the final stage of the Middle Game (93%).

3 up with hammer: In an 8-end game, anytime you are in this position you shouldn’t lose. In a 10 end game – just get past the 3rd and it would take a monumental collapse to lose (though we’ve all been there once or twice).

Battle For Hammer?

To try to answer our original question, we need to define what is meant by “Battle for the Hammer”.

Let’s assume “Battle for Hammer” implies a team which starts with hammer wishes to keep it and the opposition is trying to gain that position (tied with hammer). The advantage of tied with hammer is only slight, roughly 60 to 40, until the End Game. Teams who win 60% of their games don’t often place high in the money and they certainly don’t win Briers or Olympic Gold. We don’t gain a substantial position until the final end, where we still lose 1 of every 4 games. By this definition, I’d suggest Curling is not a Battle for Hammer.

Now, if assume we this phrase to mean a battle to gain hammer with the lead, then it could be argued Curling is a Battle for Hammer. 1 up with hammer with 8 ends remaining is the same as tied with hammer at the end of the game (75%)! Having hammer with a lead of 2 or more points is very strong. It is preferred to 3 up without during every stage of a game, except for the final end where both positions are equal.

How Important is the Hammer?
So how do we begin to analyze the importance of last rock? At any time during a game we can determine its statistical value. We’ve determined that leading with hammer is a strong position, stronger than being further ahead without hammer. But by how much? Let’s compare tied and 1 up without, 1 up with and 2 up without, and 2 up with versus 3 up without.

Tied with hammer vs. 1 up without hammer
Often, in a tie game, when a team is forced to 1 we state the opposition has done their job and taken away control. However, stats show us that there is only a small difference between tied or 1 up without
During the Early Game the difference is about 2-3%. It jumps to 5% at the beginning of the 5th end, or Middle Game. Then ranges between 0-3% until the last end where it jumps to 12% advantage for tied with hammer.

1 up with hammer vs. 2 up without hammer
When 1 up with hammer you are stronger than 2 up without by 2-4% until 4 ends remain, where it reverses to 1% advantage when 2 up, then back to advantage of 4% to 2% then 0% for the final end.

2 up with hammer vs. 3 up without hammer
Again, up with hammer is slight advantage, usually only 1% with the exception of 7 or 4 ends remaining where it is 3-4%. In real terms, these two positions are essentially equal.

So, what does this mean?
There is clearly not a significant difference in each of these scenarios. In each case having hammer while up is a slight advantage, but usually only 2-4%. Therefore, I disagree with the theory that Curling is a Battle for Hammer. Take, for example, an 8-end game where you have hammer and are held to one in the first end. Instead of having a 60% winning percentage you drop to 58%. Your position is in fact not much different than where you were at the beginning of the game. Much more significant is to have a shot for one and instead give up a steal in the first end, going from 58% to 42%.

Interesting to point out that often when the team without hammer holds the opposition to one in the first end it is perceived they have “won” the end or done their job. In reality, they have only gained a 2% advantage from where they were. More correct perhaps to state they have successfully “avoided” the position of falling behind by two or more.

Next article I will be revealing data on the Women’s Game and also attempt to tackle the question of what is “Control”.